No, it is not possible for an object to reach or exceed the speed of light, whether it is inside a black hole or in any other scenario. According to our current understanding of physics, as described by Albert Einstein's theory of relativity, the speed of light in a vacuum is an absolute limit that cannot be surpassed by any material object or information.
Black holes are extremely dense objects with a gravitational pull so strong that nothing, including light, can escape from their event horizon (the boundary beyond which nothing can return). Within the event horizon, space and time become highly distorted, and the gravitational forces are immense. These gravitational forces near the black hole's singularity (a point of infinite density) cause a severe curvature of spacetime, resulting in a one-way path toward the singularity.
As an object approaches the event horizon of a black hole, the gravitational time dilation becomes increasingly significant, which means that time appears to slow down for the object relative to observers outside the black hole. However, no matter how close an object gets to the event horizon, it will still experience time and remain within the bounds of the speed of light. In other words, the object's velocity, as measured by an outside observer, will always be less than the speed of light, regardless of its position inside the black hole.